Two-dimensional field theories deformed by Zamolodchikov's TTbar operator have recently attracted the attention of theoretical physicists due to the many important links with string theory and AdS/CFT. In this talk, I will describe various classical and quantum aspects of this particular irrelevant perturbation, including its geometrical interpretation at the classical level. I will also introduce a generalisation of this geometrical framework to 4D field theories, and discuss some of the interesting differences with the 2D case. ---- Part of London Integrability Journal Club. If you are a new participant, please register filling the form at integrability-london.weebly.com. The link will be emailed.